How to use Displace and Solidify modifiers to produce constant thickness
You can use custom vertex groups in the Solidify and Displace modifiers in order to keep the inner surface intact.
First add a vertex group to your mesh.

In the solidify modifier, expand the Output Vertex Group foldout, and set the Shell group to be your new vertex group.
Also, in the displace modifier, set the vertex group field. You might need to invert the effect with the double sided arrow next to the field.

Result (with a subdivided plane for simplicity)

On Suzanne (probably not the best model for that since there is a lot of mesh intersection but I hope you get the point)